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📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 An investor splits $50,000 between two accounts: 4% and 6% annual interest. If total interest is $2,600, how much was invested at 6%?

📌 Let \(x\) = amount at 6%, then \(50,000 - x\) at 4%.

📌 Interest: \(0.06x + 0.04(50,000 - x) = 2,600\).

📌 \(0.06x + 2,000 - 0.04x = 2,600\) → \(0.02x = 600\) → \(x = 30,000\).

📌 #### 30000Question: In a right triangle, the radius of the inscribed circle is $ r $, and the hypotenuse is $ h $. If the two legs are in the ratio $ 3:4 $, find the ratio of the area of the circle to the area of the triangle in terms of $ r $.

📌 Let the legs of the right triangle be $ 3k $ and $ 4k $, so the hypotenuse is $ h = 5k $ by the Pythagorean theorem.

📌 The inradius $ r $ of a right triangle is given by the formula:

📌 r = \frac{a + b - c}{2}

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